Analytical regularization method for electromagnetic wave diffraction by axially symmetrical thin annular strips
A new mathematically rigorous and numerically efficient method based on the combination of Orthogonal Polynomials Method, and Analytical Regularization Method, for electromagnetic wave diffraction by a model structure for various antennae such as Fresnel zone plates is proposed. It can be used as validation tool for the other (more general or less accurate) numerical methods and physical approaches. The initial boundary value problem is equivalently reduced to the infinite system of the linear algebraic equations of the second kind, i.e. to an equation of the type (I+H) x=b in the space l2 with compact operator H. This equation can be solved numerically by means of truncation method with, in principle, any required accuracy. Numerical results show that physical optics approximation may not be valid, especially in diffraction by sources other than plane wave, as it does not take into account the contribution of strip edges and interaction of strips by means of traveling slow waves.
Anahtar Kelimeler:
Analytical Regularization, Annular Strips, Antenna, FresnelZone Plates, Integral Equations.
Analytical regularization method for electromagnetic wave diffraction by axially symmetrical thin annular strips
A new mathematically rigorous and numerically efficient method based on the combination of Orthogonal Polynomials Method, and Analytical Regularization Method, for electromagnetic wave diffraction by a model structure for various antennae such as Fresnel zone plates is proposed. It can be used as validation tool for the other (more general or less accurate) numerical methods and physical approaches. The initial boundary value problem is equivalently reduced to the infinite system of the linear algebraic equations of the second kind, i.e. to an equation of the type (I+H) x=b in the space l2 with compact operator H. This equation can be solved numerically by means of truncation method with, in principle, any required accuracy. Numerical results show that physical optics approximation may not be valid, especially in diffraction by sources other than plane wave, as it does not take into account the contribution of strip edges and interaction of strips by means of traveling slow waves.
Keywords:
Analytical Regularization, Annular Strips, Antenna, FresnelZone Plates, Integral Equations.,
___
- S. M. Stout-Grandy, A. Petosa, I. V. Minin, O. V. Minin, J. Wight, A Systematic Study of Varying Reference Phase in the Design of Circular Fresnel Zone Plate Antennas, IEEE Transactions on Antennas and Propagation. Vol 54, No. 12, December 2006, 3629- 3636.
- Y. Ji, M. Fujita, Design and Analysis of a Folded Fresnel Zone Plate Antenna, International Journal of Infrared and Millimeter Waves, Vol.15, No: 8, 1994.
- G. C. Hsiao and R. E. Kleinman, Mathematical Foundation for Error Estimation in Numerical Solutions of Integral Equations in Electromagnetics, IEEE Transactions on Antennas and Propagation, Vol. 45, No: 3, 1997, 316-328.
- A. G. Dallas, G.C. Hsiao and R.E. Kleinman, Observations on the numerical stability of the Galerkin method, Adv. Comput. Math. 9 (1998) 37-67.
- G. L. Hower, R. G. Olsen, J. D. Earls, and J.B. Schneider, Inaccuracies in Numerical Calculation of Scattering near Natural Frequencies of Penetrable Objects, IEEE Transactions on Antennas and Propagation, Vol 41, No 7, July , 982-986. C. A. J. Fletcher, Computational Galerkin Method, Springer-Verlag, 1984.
- E. V. Zakharov, Yu. V. Pimenov, Numerical Analysis of Radio Waves (in Russian), Radio i Sviaz’ Publishing House, Moscow, 1982.
- G. A. Grinberg, Yu. V. Pimenov, On Electromagnetic Wave Diffraction By InŞnitely Thin Perfectly Conducting Screens (in Russian) – Zhurnal Teknicheskoy Fiziki, series B, Vol 27, 1957 No 10, pp. 2326-2339.
- G. A. Grinberg, A new method for solving problems related to diffraction of EM waves by a plane with an unbounded straight slit, Journal of Technical Physics, USSR, Vol. 27, 2595 – 2605; 1958; translation in Journal of American
- Institute of Physics, Vol. 2, 1959, 2410 – 2419.
- G. Ya. Popov. Contact problem for linear-deformable basis. Kiev, Odessa, Vyscha shkola, 1982 (in Russian).
- C. M. Butler, General Solutions of the Narrow Strip (and Slot) Integral Equations, IEEE Transactions on Antennas and Propagation, Vol. 33, No. 10, October 1985, 1085-1090.
- V. P. Shestopalov, Yu. A. Tuchkin, A. Ye. Poyednichuk and Yu. K. Sirenko, Novel Methods for Solving Direct and Inverse Problems of Diffraction Theory, vol 1: Analytical Regularization of Electromagnetic Boundary Value Problems, Kharkov: Osnova, 1997 (in Russian).
- V. P. Shestopalov and Y. V. Shestopalov. Spectral theory and excitation of open structures. IEE Electromagnetic Waves Series 42, 1996
- A. Ye. Poyedinchuk, Yu. A. Tuchkin, V. P. Shestopalov, New Numerical – Analytical Methods in Diffraction Theory, Mathematical and Computer Modeling, Vol 32, 2000, 1029-1046.
- Y. A. Tuchkin, E. Kara¸cuha, F. Dikmen, Scalar Wave Diffraction by Perfectly Conductive InŞnitely Thin Circular Ring, Elektrik, Turkish Journal of Electrical Engineering and Computer Science, TUBITAK Doga Series, Vol 9, No: 2 2001, 199-220.
- E. ¨Ozkan, F. Dikmen, Y. A. Tuchkin, Scalar Wave Diffraction by Perfectly Soft Thin Circular Cylinder of Finite Length; Analytical Regularization Method, Elektrik, Turkish Journal of Electrical Engineering and Computer Science, TUBITAK Doga Series, Vol 10, 2002, 459-472
- Yu. A. Tuchkin. Scalar wave diffraction by axially symmetrical toroidal screens. URSI-98, Proceedings of Interna- tional Symposium URSI Commission B, May 25-28, R. Kress, Linear Integral Equations, Springer, 1999.
- D. Colton, R. Kress, Integral equation methods in scattering theory, Wiley, 1983.
- L. V. Kantorovich, G. P. Akilov, Functional Analysis in Normed Spaces, (Translated from the Russian by D.E. Brown [and] Edited by A.P. Robertson), Pergamon Press Inc. (1964).
- S. G. Krein, ”Linear differential equations in Banach space”, Transl. Math. Monogr., 29, Amer. Math. Soc. (1971)
- (Translated from Russian). A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev. Integrals and series. Elementary functions, (v.1). Moscow, Nauka, ,798 p. K. F. Warnick, W. C. Chew, “On the spectrum of the electric Şeld integral equation and the convergence of the moment method” Int. J. Numer. Meth. Engng 51:31-56, 2001
- G. Fikioris. “A Note on the Method of Analytical Regularization”. IEEE Antennas and Propagation Magazine, Vol. , No 2, pp 34 – 40, April 2001
- A. I. Nosich. The Method of Analytical Regularization. IEEE Antennas and Propagation Magazine, Vol. 41, No 3, April 1999, 34 – 49.
- ISSN: 1300-0632
- Yayın Aralığı: Yılda 6 Sayı
- Yayıncı: TÜBİTAK
Sayıdaki Diğer Makaleler
Polymorphic worm detection using strong token-pair signatures
Burak BAYOĞLU, İbrahim SOĞUKPINAR
Parameter identification of a separately excited dc motor via inverse problem methodology
Mounir HADEF, Mohamed Rachid MEKIDECHE
Fatih DİKMEN, Yury Alexanderovich TUCHKIN
PCA based protection algorithm for transformer internal faults
Erdal KILIÇ, Okan ÖZGÖNENEL, Ömer USTA, Dave THOMAS
An intelligent face features generation system from fingerprints
CDM based controller design for nonlinear heat exchanger process